How do I keep a cloth simulation from interacting with a particle emitter, while still interacting with the particles?
You can do as follows:


Add a loop cut right in between the cube (cloth).
Delete the following lines:

Change the "Element to Snap to" to vertex.
Then Extrude the following highlighted lines towards the middle while stopping at each loop cut:



If all steps are done correctly the bag should open up like this:


NOTE: The more lines you delete in step 2 the wider the bag will open up.

BTW Here is the solved file: